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Copiapo, Chile (CNN) -- The painstaking process of hoisting 33 miners trapped nearly a half-mile below ground for more than two months in northern Chile was completed Wednesday night, less than a day after it began, ending a saga that gripped a nation that never gave up hope.

"I hope this will never happen again," said the last man out of the gold and copper mine, shift foreman Luis Urzua, upon reaching the surface, as he was embraced by Chilean President Sebastian Pinera. "I'm proud of being Chilean."

Rescue worker Manuel Gonzalez, the last person still in the mine, was hoisted to the surface around 11:30 p.m. ET.

It was Urzua, 54, who first established contact with the outside world on August 22, 17 days after the mine collapsed on August 5, trapping him and his men.

It was Urzua who divided the cans of tuna that helped keep the men alive until they were discovered, and it was he who organized the 32 others into three work shifts.

It was he who pored over diagrams that helped rescuers plan the men's escape, and it was he who insisted on being the last of the trapped men to be freed.

"He was a shift boss who made us proud," Pinera told Chileans in a televised address afterward. "I want to thank the families of the miners who maintained faith -- this faith that ended up moving mountains."

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Video: Miners emerge after months underground

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Gallery: Breakthrough at Chile mine

"Mission accomplished, Chile," read a sign held by one of the six rescuers who had descended more than 2,000 feet to organize the men's exodus from the mine that collapsed August 5. The six were themselves hoisted out after the 33 miners had been extracted.

Pinera put the price of the rescue mission at $10 million to $20 million. "Every peso was well spent," he said.

And he criticized the mine, saying it "never should have functioned as it was functioning; it had a long history of violations."

He added, "I want to announce to the Chilean workers and the employers that we are going to make a new pact in which the life, dignity and protection of workers will be the focus of government concern."

Representatives of the owner, the San Esteban Mining Co., have said previously they will collaborate fully with Chilean authorities and the Chilean Congress in their inquiries about what went wrong at the mine.

After 69 harrowing days, the miners ascended to freedom one by one in a rescue mission that began in the numbing chill of a desert night, continued under the searing sun of a cloudless day and stretched back into the night.

Each time the red, white and blue metal capsule approached the earth's surface, its cargo was heralded by the wail of a siren and applause from relatives and rescuers assembled nearby.

Some of the miners signaled a thumbs-up. Others waved Chilean flags. One led the crowd in a chant for Chile. Some dropped to their knees and prayed. Mostly, though, they embraced their families.

Pinera called the mission "magical." U.S. President Obama called it a "tremendously inspirational story."

Franklin Lobos, the 28th man to make the journey, arrived as dusk was falling and was embraced by his teenage daughter Carolina. "Don't make me cry," the former professional soccer player told her in a comment picked up by a microphone. She then handed him a soccer ball that he kicked around playfully for a moment.

"You have won the best and the toughest match of your life," Pinera told him as they embraced. "The match of life."

To that, Lobos responded, "The hardest of my life," then lay down on the gurney -- still clutching the ball -- and was wheeled into the adjacent field hospital for an initial examination prior to his flight by helicopter to San Jose Hospital in nearby Copiapo.

During the course of the day, the pace of the rescues increased from one per hour to three, progress that was measured by the spinning of the metal wheel that let out and then shortened the cable attached to the capsule -- a makeshift elevator with only two stops.

The job of hoisting the miners was completed late Wednesday, 22 hours and 36 minutes after it began. Prior to beginning the work, the experts had predicted the rescues would take 36 hours.

Throughout the process, Pinera stood outside the hole, greeting each arrival with a warm embrace. "We had promised to look until we found them," Pinera said. "We can all feel proud to be Chilean."

We had promised to look until we found them. We can all feel proud to be Chilean.--Chilean President Sebastian Pinera

Chilean Mining Minister Laurence Golborne -- who was a ubiquitous presence during the rescue preparations and has emerged as a popular figure in Chile -- also greeted each miner. The embraces began in the initial minutes of Wednesday with the arrival of Florencio Avalos, who was the first to step out of the "Fenix-2" capsule, named for the mythical bird that rose from ashes.

He beamed as his feet touched the surface of the earth that had held him captive, then cradled his son and wife before Pinera bear-hugged him.

The 31-year-old miner served as a cameraman during the group's isolation, shooting videos of the miners that were sent up to rescuers and relatives at the surface.

"I'm overwhelmed with emotion because it's been so long since we have seen him," Alfonso Avalos, Florencio's father, told Chile's TVN. "I'm very proud of him. Thanks to God he got out and looks good."

The night passed before it was 63-year-old Mario Gomez's turn. A miner since he was 12, he had contracted lung disease and lost three fingers in the years prior to the mine collapse. He had planned to retire but went back down in the mine that day to test drive a new truck.

His wife, Lillian Ramirez, stood by nervously as he emerged before her in the steel capsule no wider than the span of his shoulders.

Gomez, whose wife said he used to ask her to quit bugging him to say daily prayers, dropped to his knees to praise God. At that moment, she knew how fortunate she was to have him returned to her, she said.

To say there were 33 trapped in the mine is wrong, Ramirez said. There were 33 men -- and God.

Ramirez was just one of many family members who bit their lips as each man began his ascent, then broke into smiles as they emerged. But the rejoicing was loud throughout Chile and the world.

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In the capital, Santiago, hundreds wept and embraced as they watched the rescue on a flickering big screen TV set up in a square. Corks popped and champagne flowed at the Chilean Embassy in Washington.

The scene repeated itself as more and more miners arrived. Around the world, strangers sat glued to television sets.

"I mentioned on Twitter how 41 years ago the world watched men walk on the moon," said Connie Preti of New York. "Today we are seeing men come out from the earth. It's equally striking."

Close attention was paid to meeting their medical needs.

"Things are extraordinarily well, better than expected," Chilean Health Minister Jaime Manalich told reporters Wednesday afternoon, by which time 17 of the miners had reached the hospital, where each underwent a battery of tests that included a chest X-ray, an electrocardiogram, a heart echocardiogram, a dental exam, a nutritional evaluation, a skin test, an eye exam, a psychological exam and a psychiatric exam "if it's necessary."

One of the miners was admitted to the hospital's intensive care unit with pneumonia, Manalich said. "It's possible that we may have to prolong his stay," said Manalich, who would not identify the miners with health problems.

Two of the miners were expected to undergo "extensive dental surgery" Thursday. They were expected to require general anesthesia, he said.

In general, though, the miners "really are in good condition -- emotional condition and physical condition," he said. Some of them may be able to leave the hospital Thursday afternoon, he said.

Outside the hospital in Copiapo, cries of joy could be heard coming from inside as the last of the miners were freed. Chants of "Chi! Chi! Chi! Le! Le! Le!" rang from the hospital windows.

Hospital workers in the parking lot said the miners were watching the coverage of the rescues and celebrating as their friends were pulled from the mine's depths.

As the second miner, Mario Sepulveda, left the rescue hole, he reached into a large yellow bag and handed out what appeared to be rocks to officials and rescue workers.

Sepulveda cracked jokes and led the crowd in a cheer for Chile. As the 40-year-old was hauled away on a stretcher for medical evaluation, he asked his wife, "How's the dog?"

Later, in a video conference, he said his time underground had changed him.

"I buried 40 years of my life down there, and I'm going to live a lot longer to be a new person," he said. "I think I have learned a lot of wonderful lessons about taking the good path in life. For those of you able to call your wives, or your husbands, do so."

Amid the sea of Chilean flags greeting the emerging miners was a collection of small, handheld Bolivian flags for Carlos Mamani, the lone Bolivian miner.

His family back home was restrained in their emotions for much of the morning while watching the rescue on TV. But they jumped up and clapped when they saw him kneel on the ground.

Next up was the youngest of the lot: Jimmy Sanchez, an 18-year-old who worked as an environmental assistant and is the father of a newborn girl.

The 12th miner to be rescued, Edison Pena, was no longer "All Shook Up," as the Elvis Presley song goes. An Elvis fanatic who led the trapped miners in sing-alongs, Pena, 34, looked fit and exuberant. He waved and shook hands and hugged colleagues, loved ones and dignitaries.

Prior to making their ascent, each of the miners donned green coveralls made of moisture-resistant material and personalized with their names.

Each stepped into the capsule, which was equipped with communications equipment and a supply of oxygen. Each wore sunglasses to protect his eyes -- which had become accustomed to the darkness of the caved-in mine.

The, each awaited the order to hoist to begin his journey to the lights above.

The first miners to reach the surface were deemed the most fit, but also possessed the most technical know-how so that they could advise the rescue teams.

The next five were the physically weakest, a term perhaps not appropriate for anyone who has survived more than two months in the bowels of the earth. But one of the miners has diabetes; another has black lung. The miner with pneumonia was given a face mask connected to an oxygen tank, Manalich said.

For the men, the only contact with the outside world since the cave-in had been via a small bore hole through which rescuers dropped food, water and other supplies.A letter sent by one of them said they had vowed never to fully reveal the details of their underground misery.

High above the miners, family members and 1,500 journalists from 39 nations held their collective breath as the rescue mission continued throughout the day and into the night.